量子积分的Ostrowski型不等式  

Ostrowski type inequalities for quantum

作　　者：时统业[1] SHI Tongye(Naval Command College of People’s Liberation Army,Nanjing Jiangsu 211800)

机构地区：[1]中国人民解放军海军指挥学院,江苏南京211800

出　　处：《首都师范大学学报（自然科学版）》2023年第4期9-17,共9页Journal of Capital Normal University：Natural Science Edition

摘　　要：针对一阶q导数有界的函数,利用q微积分平均值不等式,建立了q-Ostrowski不等式,加强了已有文献给出的q-Ostrowski不等式,并将结果移植到qb积分。针对一阶q导数和一阶qb导数都有界的函数,利用q微积分平均值不等式,建立了同时涉及q积分和qb积分的Ostrowski型不等式,推广了经典的Ostrowski不等式。针对二阶q可微且二阶qb可微的函数,利用恒等式,通过引入参数求最值,建立了同时涉及q积分和qb积分的Ostrowski型不等式。In this paper,q-Ostrowski inequality is established for functions with bounded first order q-derivatives by means of mean value inequality for q-calculus,which strengthens q-Ostrowski inequality given in previous literature,and the result is transferred to qb-integral.Ostrowski inequality involving both q-integral and qb-integral is established for functions with bounded first order q-derivatives and qb-derivatives,and the classical Ostrowski inequality is generalized.For second order q-differentiable and second order qb-differentiable functions,using the identities and the method of introducing parameter to find the minimum,Ostrowski type inequality involving both q-integral and qb-integral is established.

关 键 词：Ostrowski型不等式 q积分 qb积分 量子微积分平均值不等式 

分 类 号：O178[理学—数学]